Question

The expression $E=\frac{1}{cosec\theta -cot\theta }-\frac{1}{sin\theta }$ is equal to which of the following expression?

• A. sinθ
• B. cotθ
• C. - cot θ
• D. sec θ
• E. tanθ

Answer 1

The correct option is B

cotθ

We have,

$\begin{array}{c}E=\frac{1}{\frac{1}{sin\theta }-\frac{cos\theta }{sin\theta }}-\frac{1}{sin\theta }\\ =\frac{sin\theta }{1-cos\theta }-\frac{1}{sin\theta }\\ =\frac{1+cos\theta }{sin\theta }-\frac{1}{sin\theta }\\ =\frac{cos\theta }{sin\theta }=cot\theta \end{array}$